A Wiki for Mizar: Motivation, Considerations, and Initial Prototype

  • Josef Urban
  • Jesse Alama
  • Piotr Rudnicki
  • Herman Geuvers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6167)

Abstract

Formal mathematics has so far not taken full advantage of ideas from collaborative tools such as wikis and distributed version control systems (DVCS). We argue that the field could profit from such tools, serving both newcomers and experts alike. We describe a preliminary system for such collaborative development based on the Git DVCS. We focus, initially, on the Mizar system and its library of formalized mathematics.

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References

  1. 1.
    The Archive of Formal Proofs, http://afp.sourceforge.net/
  2. 2.
  3. 3.
    Corbineau, P., Kaliszyk, C.: Cooperative repositories for formal proofs. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573, pp. 221–234. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Cruz-Filipe, L., Geuvers, H., Wiedijk, F.: C-CoRN, the Constructive coq Repository at Nijmegen. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 88–103. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    D’Silva, V., Kroening, D., Weissenbacher, G.: A Survey of Automated Techniques for Formal Software Verification. IEEE Transactions on Computer-aided Design of Integrated Circuits and Systems 27(7), 1165–1178 (2008)CrossRefGoogle Scholar
  6. 6.
    Git - fast version control system, http://git-scm.com/
  7. 7.
    Gonthier, G.: Formal proof—the four-color theorem. Notices of the American Mathematical Society 55(11), 1382–1393 (2008)MATHMathSciNetGoogle Scholar
  8. 8.
    Hales, T.: A proof of the Kepler conjecture. Annals of Mathematics 162(3), 1065–1185 (2005)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hales, T.: Formal proof. Notices of the American Mathematical Society 55(11), 1370–1381 (2008)MATHMathSciNetGoogle Scholar
  10. 10.
    Harrison, J.: Formal Proof – Theory and Practice. Notices of the American Mathematical Society 55, 1395–1406 (2008)MATHMathSciNetGoogle Scholar
  11. 11.
    Klein, G., Elphinstone, K., Heiser, G., Andronick, J., Cock, D., Derrin, P., Elkaduwe, D., Engelhardt, K., Kolanski, R., Norrish, M., Sewell, T., Tuch, H., Winwood, S.: seL4: Formal verification of an OS kernel. In: Anderson, T. (ed.) Proceedings of the 22nd ACM Symposium on Operating Systems Principles, pp. 207–220. ACM Press, New York (2009)CrossRefGoogle Scholar
  12. 12.
  13. 13.
    Wolfram MathWorld: The Web’s Most Extensive Mathematics Resource, http://mathworld.wolfram.com/
  14. 14.
    Matuszewski, R., Rudnicki, P.: MIZAR: the first 30 years. Mechanized Mathematics and its Applications 4(1), 3–24 (2005)Google Scholar
  15. 15.
    The Mizar Mathematical Library, http://mizar.org/library/
  16. 16.
    Naumowicz, A., Kornilowicz, A.: A Brief Overview of Mizar. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 67–72. Springer, Heidelberg (2009)Google Scholar
  17. 17.
  18. 18.
    The polymath blog, http://polymathprojects.org/
  19. 19.
  20. 20.
    The QED Manifesto. In: Bundy, A. (ed.) CADE 1994. LNCS (LNAI), vol. 814, pp. 238–251. Springer, Heidelberg (1994)Google Scholar
  21. 21.
    The QPQ Deductive Software Repository, http://www.qpq.org
  22. 22.
    Rudnicki, P., Trybulec, A.: On the integrity of a repository of formalized mathematics. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 162–174. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  23. 23.
    Trigdell, A.: Efficient Algorithms for Sorting and Synchronization. Ph.D. thesis, Australian National University (1999)Google Scholar
  24. 24.
    Urban, J.: MPTP 0.2: Design, implementation, and initial experiments. J. Autom. Reasoning 37(1-2), 21–43 (2006)MATHCrossRefGoogle Scholar
  25. 25.
    vdash: What is vdash?, http://www.vdash.org/intro/

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Josef Urban
    • 1
  • Jesse Alama
    • 2
  • Piotr Rudnicki
    • 3
  • Herman Geuvers
    • 1
  1. 1.Radboud UniversityNijmegenThe Netherlands
  2. 2.New University of LisbonPortugal
  3. 3.University of AlbertaEdmontonCanada

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